Question

Решите задачу в x. "Расстояние между А и В равно 165 км. От этих станций одновременно навстречу друг другу отправляются два поезда и встречаются через 1,5 ч на разъезде, который находится в 90 км от станции А. С какой скоростью идут поезда?" 1) Чему равна скорость сближения поездов? 2) Чему равна скорость поезда, следующего от станции А? 3) Каково расстояние от станции В до места встречи поездов? 4)Чему равна скорость поезда, следующего до станции В?

Answer 1

Поезда встретились в точке, находящейся в 90 км от точки А, т.е., один из поездов, который выехал из точки А, проехал 90 км за 1,5 часа, а тот, что двигался из точки В проехал 165-90=75 км за 1,5 часа.
Скорость является отношением расстояния ко времени, т.е., первый поезд двигался со скоростью 90/1,5 = 60 км/ч, а скорость второго поезда 75/1,5 = 50 км/ч.
Ответ: 60 км/ч, 50 км/ч.

Answer 2

Task: We are given that the distance between stations A and B is 165 km. Two trains depart simultaneously from these stations and meet at a junction which is located 90 km from station A. They meet after 1.5 hours. We need to find the speed of the trains, the rate of approach, the speed of the train coming from station A, the distance from station B to the meeting point, and the speed of the train going towards station B.

Solution: Let's solve the problem step by step.

1) Finding the speed of the trains: To find the speed of the trains, we can use the formula:

Speed = Distance / Time

Since the trains are traveling towards each other and meet after 1.5 hours, we can calculate the total distance traveled by both trains as the sum of the distances covered by each train:

Distance = Distance from station A to the meeting point + Distance from station B to the meeting point

Given: Distance from station A to the meeting point = 90 km Distance from station B to the meeting point = 165 km - 90 km = 75 km

Distance = 90 km + 75 km = 165 km

Using the formula, we can find the speed of the trains:

Train Speed = Distance / Time = 165 km / 1.5 hours = 110 km/h

Therefore, the speed of each train is 110 km/h.

2) Finding the rate of approach (relative speed): The rate of approach or relative speed of the trains is the sum of their individual speeds. In this case, since the trains are traveling towards each other, their relative speed will be the sum of their speeds:

Rate of Approach = Speed of Train A + Speed of Train B = 110 km/h + 110 km/h = 220 km/h

Therefore, the rate of approach of the trains is 220 km/h.

3) Finding the speed of the train coming from station A: Since the distance from station A to the meeting point is 90 km and the time taken is 1.5 hours, we can use the formula:

Speed = Distance / Time = 90 km / 1.5 hours = 60 km/h

Therefore, the speed of the train coming from station A is 60 km/h.

4) Finding the distance from station B to the meeting point: We already calculated this distance earlier:

Distance from station B to the meeting point = 75 km

Therefore, the distance from station B to the meeting point is 75 km.

5) Finding the speed of the train going towards station B: Since the distance from the meeting point to station B is 75 km and the time taken is 1.5 hours, we can use the formula:

Speed = Distance / Time = 75 km / 1.5 hours = 50 km/h

Therefore, the speed of the train going towards station B is 50 km/h.

To summarize: 1) The speed of each train is 110 km/h. 2) The rate of approach (relative speed) of the trains is 220 km/h. 3) The speed of the train coming from station A is 60 km/h. 4) The distance from station B to the meeting point is 75 km. 5) The speed of the train going towards station B is 50 km/h.